Probabilistic analysis of directed polymers in a random environment: a review
Probabilistic analysis of directed polymers in a random environment: a review
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DOI：
10.2969/aspm/03910115
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
F. Comets;T. Shiga;N. Yoshida
中科院分区：
文献类型：
--
作者：
F. Comets;T. Shiga;N. Yoshida
随机环境中的定向聚合物可以被认为是统计力学模型，其中随机过程的路径与淬灭无序（杂质）相互作用，具体取决于时间和空间。我们在这里回顾过去十五年中获得的主要结果，并对大多数结果进行证明。该材料涵盖了 J. Imbrie、T. Spencer、E. Bolthausen、R. Song 和 X. Y. Zhou 研究的弱无序相聚合物的扩散行为 [11,3, 25]，以及 P. Carmona、Y. Hu 和本文作者最近获得的强无序相路径的局部化 [4, 5]。
Directed polymers in random environment can be thought of as a model of statistical mechanics in which paths of stochastic processes interact with a quenched disorder (impurities), depending on both time and space. We review here main results which have been obtained during the last fifteen years, with proofs to most of the results. The material covers the diffusive behavior of the polymers in weak disorder phase studied by J. Imbrie, T. Spencer, E. Bolthausen, R. Song and X. Y. Zhou [11, 3, 25], and localization of the paths in strong disordered phase recently obtained by P. Carmona, Y. Hu, and the authors of the present article [4, 5].